IN LOWERING THE FREEZING POINT OF WATER. 579 
Process 4. Remove the cylinder from the lake at—?¢’, and place its bottom 
again on the non-conducing stand. Move the piston back to the position it occu- 
pied at the commencement of Process 1. The temperature and pressure, during 
this process, must vary with one another, as they did in Process 2. Also, since 
as much heat has been given out as was taken in; and since the volume is the 
same as at the commencement of Process 1, the physical state of the mass con- 
tained in the cylinder must be now in every respect the same as it was at that 
time. 
By representing graphically in a diagram the various volumes and corre- 
sponding pressures, at all the stages of the four processes which have just been 
laid down, we shall arrive, in a simple and easy manner, at the quantity of work 
which is developed in one complete stroke by the heat which is transferred during 
that stroke from the lake at 0° to the lake at—7¢°. For this purpose, let E be 
the position of the piston at the beginning of Process 1; and let some distance, 
such as EG, represent its 
stroke in feet, its area be- 
ing made a square foot, 
so that the numbers ex- 
pressing, in feet, distances 
along EG may also ex- 
press, in cubic feet, the 
changes in the contents of A 
the cylinder produced by 
the motion of the piston. Now, when 1:087 cubic feet of ice are melted, 
one cubic foot of water is formed. Hence, if EF be taken equal to -087 feet, 
F will be the position of the piston when one cubic foot of water has been melted 
from ice, that is, the position at the end of Process |, the bottom of the cylinder 
being at a point A distant from F by rather more than afoot. Let e¢/ be parallel 
to EF, and let E ¢ represent one atmosphere of pressure ; that is, let the units of 
length for the vertical ordinates be taken such that the number of them in Ee 
may be equal to the number which expresses an atmosphere of pressure. Also 
let gh be parallel to EF, and let fm represent the increase of pressure produced 
during Process 2. Then the straight lines ¢/and gh will be the lines of pressure 
for Processes 1 and 2; and for the other two processes, the lines of pressure will 
be some curves which would extremely nearly coincide with the straight lines /g 
and he. For want of experimental data, the nature of these two curves cannot 
be precisely determined ; but, for our present purpose, it is not necessary that 
they should be so, as we merely require to find the area of the figure ¢ fg h, which 
represents the work developed by the engine during one complete stroke, and this 
can readily be obtained with sufficient accuracy. For, even though we should 
VOL. XVI. PART V. tals 

